Adaptive Control

It is well known that adaptive control is an effective approach method to deal with system with unknown parameters. This chapter studies the adaptive control problem of SMJSs with general TRMs. First, an adaption law is proposed to estimate the upper bound on the unknown parameters related to uncertain TRM. Then, a class of adaptive state feedback controllers is designed, where the parameters can be obtained by solving a set of LMIs. It is shown that not only is the estimated error bounded almost surely but also the states of the closed-loop system are asymptotically stable almost surely. Moreover, the proposed adaptive controller can be extended to another general case of TRM when the bound of the unknown elements of TRM is unavailable. Based on the established methods, adaptive state estimation problem is further considered for a class of stochastic delay systems with state-dependent Markovian switching.